Given f(n)=sqrt(2n+1+2 sqrt(n^2+n)), Evaluate 1/(f(1))+1/(f(2))+1/(f(3))+...+1/(f(99))

Alfredeim 2022-09-12 Answered
Given f ( n ) = 2 n + 1 + 2 n 2 + n , Evaluate 1 f ( 1 ) + 1 f ( 2 ) + 1 f ( 3 ) + + 1 f ( 99 )
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Answers (2)

Holly Schmidt
Answered 2022-09-13 Author has 10 answers
The hint.
Use
1 n + 1 + n = n + 1 n
and the telescopic sum.
Finally, we obtain
100 1 = 9.
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lemondedeninaug
Answered 2022-09-14 Author has 2 answers
Very simple Hint: Rationalize the denominator
1 f ( x ) = 1 n + n + 1 = n n + 1 ( n + n + 1 ) ( n n + 1 ) = n + 1 n
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